How do you differentiate g(x) = (x^2+1) (x^2-3x) using the product rule? Calculus Basic Differentiation Rules Product Rule 1 Answer Jothi S. Jan 4, 2016 g'(x)=4x^3-6x^2+2x-2 Explanation: g(x)=(x^2+1)(x^2-2x) Product rule :d/dx(uv)=(du)/dxv+u(dv)/dx u=(x^2+1) du/dx=2x v=x^2-2x dv/dx=2x=2 d/dx(x^2+1)(x^2-2x)=(du)/dxv+u(du)/dx =2x(x^2-2x)+(x^2+1)(2x-2) =2x^3-4x^2+2x^3-2x^2+2x-2 =4x^3-6x^2+2x-2 Answer link Related questions What is the Product Rule for derivatives? How do you apply the product rule repeatedly to find the derivative of f(x) = (x - 3)(2 - 3x)(5 - x) ? How do you use the product rule to find the derivative of y=x^2*sin(x) ? How do you use the product rule to differentiate y=cos(x)*sin(x) ? How do you apply the product rule repeatedly to find the derivative of f(x) = (x^4 +x)*e^x*tan(x) ? How do you use the product rule to find the derivative of y=(x^3+2x)*e^x ? How do you use the product rule to find the derivative of y=sqrt(x)*cos(x) ? How do you use the product rule to find the derivative of y=(1/x^2-3/x^4)*(x+5x^3) ? How do you use the product rule to find the derivative of y=sqrt(x)*e^x ? How do you use the product rule to find the derivative of y=x*ln(x) ? See all questions in Product Rule Impact of this question 1616 views around the world You can reuse this answer Creative Commons License